XA: A non-theist need not be a naturalist in such a crude sense that all entities are physical or reducible to the physical in some sense or another (e.g., in terms of logical supervenience). One could hold a gazillion different views here. Here's the one I hold at the moment: all *contingent* being is reducible to the physical, but since abstracta exist (including moral properties), and exist of metaphysical necessity, then they need no causal or explanatory ground in terms of the physical; nor, for the same reason, need they be caused or explained in terms of a god (being the necessary beings they are). If this is plausible -- and I think it obviously is -- then (2) is implausible. On the other hand, if you're just dead set on characterizing physicalism so that it requires the reducible of everything to the physical, then since the alternative view I mention is plausible, then (1) is implausible (well, it's implausible anyway; this is just an extra reason for thinking so).
Here's the problem I have with all of this. You have the physical world, which is a closed system of physical causes. I take it that all contingent states, on this view, can be explained from the stand point of the closed and mechanistic physical order, and by whatever supervenience relations obtain. And there are the necessary moral truths, which do not rely on anything, God or the physical, for their existence. The trouble is that for Plato himself, we have a soul, which had a previous existence, and had a direct awareness of the Forms, but now that we are encased in fleshly bodies, we forgot all that knowledge of the Forms, unless it is somehow brought out of us through midwifery of some kind. In other words, Plato postulated some kind of interconnection between the world of forms and how our thoughts get caused in the real world. The Augustinian doctrine of divine illumination is the Christian replacement for the Platonistic doctrine of recollection. But this view you're propounding doesn't have any conduits from the truths of morality to the real world of our experience. If our duties are determined by the abstracta, then we may be able to act in accordance with duty, but we certainly can't act from duty, as Kant would say. If we act morally, the morality of our actions is at best epiphenomenal. Our state of acting rightly would be determined by whatever state the physical was in, and would not be determined by the state of what is morally true. I think this makes the position thus sketched wildly implausible.